I downloaded a live ISO of Sabayon 13.08 amd64 GNOME. I tried booting it using a USB in my laptop which is a Sony Vaio E series (Core i5, 4GB RAM) which came preinstalled with Windows 8. The problem is that it boots Sabayon but after letting me choose what i want to do (whether i choose "Install" or "Live CD") the screen just goes black and nothing happens.

I tried booting it in a different laptop which had Windows 7 in it and it worked.

While installing it in Sony laptop, i disabled "Secure boot" and also chose the boot as "Legacy" instead of "UEFI".

UEFI & Secure Boot are a hassle for many Linux distributions. But as you describe your situation it does not seem to be related to UEFI.

You have not installed Sabayon on your laptop so far, but you tried to boot either a Live system or "boot" right into the installer which both failed? Have I understood you correctly?According to your post, the problem seems to be the graphics/display settings not UEFI stuff, as Sabayon boots but stops at a certain point?!